How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3?
Started 4 days ago by Shashank in
Explanatory Answer
3 cases:
• 7 is in first place: 3 can go to 3 places, remaining 2 places will have 8 & 7 possibilities each
Hence, possible numbers are 3*8*7 = 168
• 7 is in second place: 3 can go to 2 places, first place will have 7 possibilities (excluding 0), and
remaining place will also have 7 possibilities
Hence, possible numbers are 2*7*7 = 98
• 7 is in third place: 3 can only go to one place, remaining 2 places have 7 possibilities each
Hence, possible numbers are 1*7*7 = 49
Therefore, total number of possibilities are 168 + 98 + 49 = 315
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